At least in terms of other 19-nor derived steroids (nandrolone), several authors have concluded that the ester alters the effects*:
"We conclude that the side-chain ester and the injection site and volume influence the pharmacokinetics and pharmacodynamics of nandrolone esters in an oil vehicle in men."
J Pharmacol Exp Ther. 1997 Apr;281(1):93-102.
Pharmacokinetics and pharmacodynamics of nandrolone esters in oil vehicle: effects of ester, injection site and injection volume.
Furthermore, most steroids have poor solubility in either water or oil. Esterifying them improves oil solubility, as an ester is simply a fatty acid chain. The longer the chain, the better the oil solubility, and the more time it takes to disperse into your blood.
Ergo, longer esters are more slowly absorbed. This creates less of a spike in blood levels and usually less side effects (as it stays under a given threshold where those side effects would occur)...even at the same milligram level of the actual hormone.
Again, looking at Nandrolone, it's even been observed that differing anabolic/androgenic ratios can be had if the steroid is administered with a similar dosing protocol irrespective of ester.*
I.E. if you shoot 400 mgs of testosterone with no ester (also called testosterone suspension ...ouch!), you'll get almost no anabolic effects....but if you shoot 400 Mgs of Testosterone Undecanoate (a very long acting testosterone), it'll release over a very long time, and you'll be able to take advantage of it's effects for awhile.
The testosterone suspension will be gone in a day and no new muscle will have been added...while you'll probably get some kind of anabolic effect from the testosterone undecanoate over the course of 2-3 weeks.
Distribution coefficients and anabolic activities of some nandrolone esters.
J Pharm Pharmacol. 1972 Dec;24:Suppl:174P.
A Hansch analysis of the anabolic activities of some nandrolone esters.
J Med Chem. 1974 Feb;17(2):157-61
So the answer is yes, the ester will alter the side effects and anabolic effects of the drug. However, if you keep doses below a certain threshold, and insure stable blood levels of the compound either with a longer ester or consistent small doses of a more shortly estrified product, then the anabolic effects and side effects will be the same regardless of ester.
(In other words, if you compensate for the ester with a specific dosing protocol, you will get the same results regardless of it's length as compared to other formulas of the same base compound, but with a different ester)