Hybrids are usually more resistant to certain diseases, but that doesn't mean they are necessarily easier to grow. Heirlooms on the other hand can be more prone to disease and climate factors.
Even though all tomatoes have similar requirements in terms of growing conditions, there are variations with different varieties, so you should choose the ones that can thrive in the conditions in your area (temperature, length of growing season, precipitations, potential disease breakouts occurring in the area etc.)

All tomatoes are suseptble to disease that blows in on the wind, like fungus, blight, etc. Hybrids, for the most part have some known resistance to soil born disease, like wilts. Many heirlooms actually have resistance also but since there is no money to be made in open pollinated seeds, no one pays for the testing to determine disease resistance. Many of the newer hybrids are offering disease packages that include virus spread by insects and, in some cases late blight. I was never aware of any difference in vigor between heirloom and hybrid tomatoes, although hybrid tomatoes seem to produce more tomatoes than heirlooms, as a rule.

pale, droopy, yellowed leaves

Are not normal for any tomato plant - hybrid or heirloom - so something else is going on. Whether it is a disease or something else entirely we would need much more info and a picture would help.

Keep in mind that "All conditions are the same otherwise." is often very subjective and there are variables we are unaware of.

Dave

I will see about posting pics.

Agree about the "all conditions" statement, but it really is as close as can possibly be.
All plants were started from seed in the same medium, same conditions, at the same time.
Hardened off in the greenhouse and outside at the same time.
All are planted in the same raised bed, were planted at the same time, and are watered with a PVC drip irrigation system so are receiving similar water.

The one issue is that the plants were larger than I would like when planted; I am thinking the heirlooms have not adapted to the stress of transplanting as well.

My answer to your question would be...No. Heirlooms are
no easier nor harder to grow than hybrids. Equal treatment
of plants should equal the same results no matter if it's
heirloom or hybrid.

How long has this condition been going on?

Have you checked your PVC drip irrigation? Those things
can be prone to clogging. Make sure your plants are
getting the water you think they should be getting.

I don't think the size of the plants being larger than you
liked comes into the equation. Larger plants should
resist stress better than small plants.

Larger transplants don't tolerate transplant shock nearly as well, true, but once they adjust we often find pockets of poorly draining or quickly soil, water pooling in low spots, pockets of soil pests, unusual unanticipated shade in spots, etc.

Dave

It has to be an issue with water or specific spots. Just recently my container plants showed stress (waited too long to water) across multiple varieties of heirlooms and hybrids. My raised bed toms are all monsters, mixed hybrids and heirlooms. Now if we were talking production, I think the hybrid vs heirloom my ply in, but more importantly the variety.

As others have said, there is nothing particularly different with growing hybrids or heirlooms. Heirlooms and Hybrids can both present resistance to certain types of plant pathogens, but hybrids do have "hybrid vigor" and can sometimes tolerate a little more stressful conditions - the difference has not yet been particularly noticeable based on the heirlooms I grow.

That being said, what else is different about your plants? Did you grow them all from seed? If not, were they all purchased from the same supplier? Were they all the same size and of similar health at planting time?