The first syllable of worship is pronounced the same way that the
word were is pronounced. In contrast, the first syllable of warship is
pronounced the same way that the word wore is pronounced. Those two
sound-alike words — were, wore — are unlikely to be pronounced the same
as each other in most accents, or maybe in any.
The second syllable of worship is pronounced the same way the second
syllable of the word bishop is pronounced. In other words, it’s a very short,
unstressed syllable with a fully reduced neutral vowel, the one we call
schwa. In contrast, the second syllable of warship is pronounced almost
as though it were the full word ship. It’s a separate morpheme in
a compound word that retains its original character, and it is not reduced.
Precisely how you represent these two words phonetically very much depends
on which particular accent we’re talking about. The respective variants can
sound quite different from how each other sounds, and their corresponding
phonetic representations can often look even more unalike than the sounds.
All that variation aside, one reasonably simple representation that works
for rhotic speakers with monophthong vowels before rhotics would be to use
/ˈwəɹʃəp/ for worship and to use /ˈwoɹˌʃɪp/ for warship. Notice how the
second of those has a bit of secondary stress in its second syllable that
the first one lacks.
You should also be aware that most North American speakers, especially rhotic ones,
neutralize the lax–tense (or open–close) phonemic distinction (/ɔ‑o/, /ɛ‑e/) before
rhotics, perceiving each to always be the close variant in that position.
That makes wore have the same tense /o/ vowel as woe has for them, not
the lax /ɔ/ vowel they have in the word wall.