Carbon seatposts likely produce the most vibration damping
There have been at least two lab tests of vibration damping in seatposts. One, by Bike Radar, tested five brands of carbon seatposts. The second, by Velonews, tested 14 seatposts, including carbon, aluminum, and titanium. In addition, the Velonews test included one traditional suspension seatpost (i.e. the Cane Creek Thudbuster), plus a few other seatposts designed to offer significant flex (e.g. a Specialized seatpost with elastomers). The Bike Radar lacked traditional suspension seatposts, but had some seatposts in the second category (i.e. non-traditional, low-travel suspension posts).
Generally, posts with saddle setback offer more damping. Carbon posts also offer more damping. The Velonews test only included two titanium seatposts, both from one manufacturer (Moots). That said, the titanium posts had slightly more damping than aluminum posts. Also, the more seatpost you have exposed, the more damping you may get (this appears to vary by seatpost model).
In general, do note that lowering your tire pressure can provide additional vibration damping. I do not know if testers have quantified this in relation to how much you might gain from a different seatpost. To answer your question, titanium might not provide much more vibration damping than an aluminum seatpost. It probably won't provide less damping. If your saddle position allows it and this is important to you, you might want to think about getting a setback post. If you must change your seatpost, you may be better off considering a carbon seatpost.
Most generally, use grease to prevent seizing
For anything titanium, i.e. titanium seatpost and/or frame, the general recommendation is to use anti-seize. I have been trying to find out what anti-seize is and why it is recommended for titanium. I believe anti-seize may be ordinary grease with additives like copper, nickel, or other substances. Titanium is prone to galling, i.e. adhesion between sliding surfaces like screw threads or seatposts. To be honest, it still is not clear to me why grease alone does not suffice to prevent galling. Nevertheless, it appears to be commonly accepted wisdom to use anti-seize on titanium. Thus, I have to keep recommending that you do so.
Anti-seize can contain copper, but it can contain other minerals instead. For example, Park Tools' anti-seize is aluminum based. I commonly see copper anti-seize recommended for titanium. I can't find any information on why copper is best for this application. There may not be any substantive reason.
For aluminum or steel seatposts in aluminum or steel frames, standard grease suffices. Oddly enough, per the Wikipedia link, aluminum is also prone to galling, and it would seem to call for anti-seize as well. Nevertheless, conventional wisdom appears to be that an aluminum seatpost in any frame with grease is fine, provided you periodically (usually at least annually) regrease it.
For carbon fiber frames and/or carbon fiber seatposts, the answer is also standard grease. If the seatpost slips, you can use carbon assembly paste, which is grease with compounds that add friction. There appears to be a myth that grease harms carbon fiber. In fact, I was about to write just that, but while searching for sources to back up that assertion, I found that Lennard Zinn, a technical writer for Velonews, and Craig Calfee, who makes carbon bikes, both have said that grease is fine in carbon frames or on carbon posts.