I don't know how much it costs to rent a power recorder, but new they start from about $1500 for something that just monitors one hot wire to well over $10,000 for Fluke 3 phase models. If you're doing an assessment, it might be worth looking into getting at least two datalogging multimeters which would allow you to record voltage fluctuations over an extended period of time. It won't be as precise as a power analyzer, but it will help.
I'm going to mention a product I've been beta testing because I think it has a lot of potential in cases like this where a customer may not see the need for the expense of full power analyzing or for little guys like me who can't afford that kind of equipment. I have three Agilent DMMs and a clamp meter, all of which have an IR port. My U1272A and U1242B both do datalogging to internal memory, but the product I just finished beta testing is the U1177A which is a Bluetooth module that attaches to any of the Agilent handhelds, and communicates with either an Android phone or Android tablet. There is software (free) that will stream data from up to three DMMs simultaneously and log it, graph it, perform math functions, and export for later analysis. Depending on which DMM you get, you can get a set of three DMMs with Bluetooth modules for as little as $300 (there's a promotion on the modules, so they're free right now with the purchase of a DMM). The avertised price for the modules is $48, so it makes sense to take advantage of the promo.
With this setup, you could easily monitor voltage of both hots in one panel plus one hot in the second panel for a 24-48 hour period. That should be enough information to decide whether there are problems with the neutral or not, or whether there are any meaningful spikes happening, as well as whether it's just affecting one panel or both.
Here's a link to a video I made that shows some of what the system does (with just the meter software):
http://www.youtube.com/watch?v=tSodrChd4iU
I'll try and do a screen shot of the datalogging software so you get an idea of what it looks like.
Disclaimer: I don't work for Agilent. I took part in a beta testing program.