I found streaming media to be tricky. Large, hi quality blu-ray rips in .mkv format stutter for some, despite gigabit wired connections and fast PCs.
My BDP, a Panasonic DMP-BDT220, can play streams, connect to DLNA servers, or play content locally (from a connected hard drive). I was not happy
with DLNA (really slow FF and rewind for one), had incurable stutter from a share, but local playback works fine. I put my 1.5 TB drive in a USB 3
enclosure, connect to the BDP and it works beautifully. I bring it to the PC to organize and load content. Not perfect, but it works. The answer to your
question I think, is; you won't know till you try, with your files, and your equipment.
Also, if your tv is just being used as a monitor, with all video inputs going through a receiver, then streaming to the BDP would be preferable.
Check the file types of the media you want to play, and see if they are supported by your device. If not, a media player would work.