(1) Statistical analysis
I collected some data on the variation between "a suspicious noun" and "a suspect noun". I collected all instances of these forms from the Corpus of Contemporary American English. I then performed a so-called distinctive collexeme analysis. This will show preference of one noun to occur with one particular adjective, either suspicious or suspect.
The following 12 nouns in my dataset are most strongly associated with suspicious (over suspect):
COLLEX O.CXN1 E.CXN1 O.CXN2 E.CXN2 ASSOC COLL.STR SIGNIF SHARED
1 LOOK 0 9.6 34 24.4 Suspicious 23.16873 ***** N
2 PACKAGE 2 14.8 50 37.2 Suspicious 22.30575 ***** Y
3 MAN 0 6.8 24 17.2 Suspicious 16.25188 **** N
4 EYE 0 6.5 23 16.5 Suspicious 15.56498 **** N
5 DEATH 0 5.1 18 12.9 Suspicious 12.14339 **** N
6 CAR 0 4.3 15 10.7 Suspicious 10.10067 ** N
7 GLANCE 0 4.0 14 10.0 Suspicious 9.42146 ** N
8 LUMP 0 3.4 12 8.6 Suspicious 8.06556 ** N
9 PERSON 2 7.1 23 17.9 Suspicious 6.58107 * Y
10 SPOT 0 2.0 7 5.0 Suspicious 4.69044 * N
11 ACTIVITIES 1 4.3 14 10.7 Suspicious 4.56712 * Y
12 FIRE 1 4.3 14 10.7 Suspicious 4.56712 * Y
In contrast, the twelve nouns below are the ones most strongly associated with suspect (over suspicious):
COLLEX O.CXN1 E.CXN1 O.CXN2 E.CXN2 ASSOC COLL.STR SIGNIF SHARED
1 LIST 20 5.7 0 14.3 Suspect 51.47099 ***** N
2 FOOD 8 2.3 0 5.7 Suspect 20.32793 ***** N
3 CLASSIFICATION 6 1.7 0 4.3 Suspect 15.21411 **** N
4 DESCRIPTION 4 1.1 0 2.9 Suspect 10.12165 ** N
5 INFORMATION 3 0.9 0 2.1 Suspect 7.58337 ** N
6 AREA 7 3.1 4 7.9 Suspect 5.96518 * Y
7 AGENT 2 0.6 0 1.4 Suspect 5.05035 * N
8 AGREEMENT 2 0.6 0 1.4 Suspect 5.05035 * N
9 COMPANY 2 0.6 0 1.4 Suspect 5.05035 * N
10 CREW 2 0.6 0 1.4 Suspect 5.05035 * N
11 DEAL 2 0.6 0 1.4 Suspect 5.05035 * N
12 DOCUMENT 2 0.6 0 1.4 Suspect 5.05035 * N
One can now use the items that are most distinctively modified by the adjectives suspect and suspicious to speculate on likely differences between the meaning of the two words.
Keep in mind that the results of such an analysis are not black and white - they do not tell you where one word is right and the other wrong, but where one word is preferred over, more likely than, the other.
Based on the data, I would propose the following two hypotheses:
Suspicious is preferred to convey that something is wrong with a circumstance obtaining in the first place. It is funny that something has occurred or is occurring at all. The whole situation surrounding a thing seems fishy. The reasons for suspicion are indirect or inferred.
Suspect is preferred to convey that there is something wrong with a particular property or properties of an entity. There is a funny feeling about a specific, tangible aspect of a thing. There is concrete evidence in the thing itself that seems fishy. The reasons for suspicion are direct or self-evident.
Consider some of the top items on the suspicious list:
"A suspicious package" is likely to mean that something is wrong about the package being there at all. The whole situation surrounding the package is odd. "Police have detonated and removed a suspicious package found on the tracks of the train station" (Why was the package on the tracks?).
"A suspect package" is likely to mean that the delivery of the package itself is not extraordinary, but it looks funny, maybe it has an odd shape, sender, or maybe it smells like cocaine. "A suspect package sent to Parliament sparked a security alert" (Why did the package look funny?).
"A suspicious death" is likely to mean that there is something funny about the fact that there was a death at all. The circumstances of the death are unusual so that people think it might have been murder.
"A suspect death" is likely to mean that the death occurring itself is not bizarre, but a specific aspect of the death is extraordinary. It's hard to exemplify what that could be. Death is death. What specific aspect of a death could possibly be unusual? A "suspect death" may actually be a somewhat odd expression.
"A suspicious lump/spot" is likely to mean that there is a growth on your body that shouldn't be there in the first place. Maybe it indicates cancer. You see a lump where a lump doesn't normally occur.
"A suspect lump/spot" is likely to mean that the presence of the lump/spot itself is not remarkable, but there is something funny about one of its specific properties. For example, if all the spots on your body are black, but one spot is red, then it could be described as "a suspect spot".
Now consider some of the top items on the suspect list:
Suspect food is likely to mean that there is a concrete property of the food that makes it worrisome. Maybe it smells funny, looks spoiled, or consist of questionable ingredients.
Suspicious food is likely to mean that nothing is wrong with the food itself, but the food is found in bizarre circumstances. Maybe a poor, homeless person was seen eating caviar. Or maybe every time you eat a food item, you notice an allergic reaction.
DESCRIPTION, INFORMATION, DOCUMENT
A suspect description etc. is likely to mean that there is a specific aspect inherent to the description itself that makes it untrustworthy. For example, it could sound too good to be true or contain information that goes against common sense etc.
A suspicious description etc. is likely to mean that the description itself is perfectly fine, but the circumstances in which it was given seem extraordinary. For example, a witness might give a normal description of an alleged criminal, but she may show up out of nowhere to volunteer the description, or she may live far away from the crime scene.
"A suspect company" is likely to mean a business that shows specific signs of misconduct, such as an unprofessional catalogue, over-priced products, or lack of a business address.
"A suspicious company" is likely to mean not that specific aspects of the company are questionable, but that the general situation surrounding the company is strange. They might do odd things, make bold claims, sell on the internet, or aggressively call people.
Animate entities are often described as suspicious, but not really as suspect, to express that they have a skeptical, suspecting attitude. One could say that suspicious is more psychological or mental than suspect.
Consider again the suspicious list:
"A suspicious man/person" can mean that the person is suspicious/skeptical about something.
Okay: His suspicious wife speculated that he was having an affair.
"A suspect man/person" is very unlikely to mean that the person suspects something.
Strange: # His suspect wife speculated that he was having an affair.
LOOK, EYE, GLANCE
There seems to be a common expression involving suspicious + look, eye or glance which, again, conveys that a person has a skeptical, suspecting attitude. Okay: a suspicious look
But suspect does not collocate well with look, eye, or glance. Strange: #a suspect look