A Google Ngram chart of "is symmetric to" (blue line) vs. "is symmetrical to" (red line) vs. "is symmetric with (green line) vs. "is symmetrical with" (yellow line) for the period 1800–2005, with smoothing 3, looks like this:
But a check of the actual matches associated with both the "is symmetric with" and "is symmetrical with" lines indicates that they are dominated by matches of the form "is symmetric/symmetrical with respect to ..." which is not the type of construction that the OP asks about. Dropping those to wordings from the chart, we get this magnified chart for "is symmetric to" (blue line) vs. "is symmetrical to" (red line), for the same time period, with the same smoothing:
This chart suggests that for much of the past century the "symmetrical" variant has been somewhat more popular than the "symmetric" variant—but that the situation has changed in recent years. At this point, usage of the two variants in published content appears to be so close that it would be difficult to argue that either form is wrong. Under the circumstances, unless I were under orders to follow an in-house word-list spelling preference, I would simply adopt the form I preferred, use it consistently, and not look back.