Whether you will truly see an improvement upgrading from your older, high quality Component player to a newer, modest quality DVI player is really tough to say.
Keep in mind that part of the answer is what's going on differently in your DISPLAY when fed data over the two different inputs.
As far as a new purchase is concerned, the digital video outputs (HDMI or DVI) bypass the analog video output stage -- the Digital to Analog Converters or DACs in the player. Generally speaking, more expensive players include better quality DACs. Since the HDMI or DVI outputs don't use that portion of the player, it is conceivable that you could get a cheaper player that still puts out a very high quality signal over the digital outputs. But odds are that a less expensive player has cut corners in other ways as well -- ways that might damage the signal going out the HDMI or DVI output. Bad de-interlace processing or scaling in the player would be the usual suspects.
Simply put, use of a modern player via HDMI or DVI to a digital display is CAPABLE of producing a better image, but by no means guaranteed. It is capable of doing so because extra digital to analog and analog to digital conversion steps are not needed and because filtering systems that soften color data, or even gray scale data, that are commonly used in analog video processing may very well not be duplicated in the digital signal path. That is, the real signal bandwidth (sharpness and resolution) may very well be greater.
But whether you will see a meaningful difference on your equipment depends on too many details to give a definitive answer.
--Bob