Upgrade player or buy a separate DAC

I've been using a Pioneer Elite 38A DVD player for both
HT and playing CD's. It's a wonderful DVD player, however
it's nothing special with redbook CD's. Would you recommend that I upgrade the player or purchase a higher
quality DAC? If you recommend the latter, what would you
suggest for $500 price point?
Thanks in advance,
ScottDixon DAC, with or without tubes. Amazing for a pittance or

BEL Canto Dac 2.0...another amazing DAC but quite a bit more expensive. You will not regret this purchase for a longtime to come.
I say go for a separate DAC. You should look into Scott Nixon's Tube DAC. Do a search for it at this forum - there have been quite few posts on this topic in the recent past. This unit is well within your price range but more importantly, it is a very well regarded DAC.
The website is scott-nixon.com
You can get his top of the line TubeDac+ while remaining within your budget.
Listen before you buy. The Pioneer is hard to beat. You will have to spend a bundle to hear a difference. Try borrowing a DAC and find out for yourself.