There's no particular reason why your MB can't do what your iPhone can. MBs tend to have plenty of horsepower for displaying video. And countless numbers of us with Apple computers do not have your problem, which probably means it's something on your end. There's many variables here. Here's a few for starters:
- Relative distances (phone close to
TV, while MB is on a desk downstairs or similar?)
- Old MB vs. new iPhone (varying wifi technologies)?
- Comparing exact same files or is MB maybe trying to send a higher res, bigger file vs. phone?
- MB maybe wired vs. iPhone using wifi? (note that wired is usually better so this would lead to questions about cables, router/switch, etc)
When you have this kind of problem, there are all kinds of possibilities. A good idea is to try to narrow down possible issues to the minimums and then systematically change variables to try to find the weak link. The cause could be as simple as a single cable.
For example, use a video you've
downloaded that has historically had streaming issues. You want to download a test video so that both devices can stream the SAME video rather than potentially having a streaming source feeding one version to one device and a different version to another device. Sync that video to your iPhone temporarily. Now that you have 2 copies of the SAME video on both devices, test playback on both devices. Does your problem persist?
Test 2: hook up the MB via ethernet to eliminate wifi issues temporarily. With potential wifi issues out of the equation, try streaming the downloaded file(s) now. Still have the problem this way? If so, check the middleman tech between your MB and your

TV, particularly router/switch. If you have alternates, slug them in and test with them. If you are confident about your router/switch hardware, swap out ethernet cables, testing with each change.
Test 3: rule out that it's your

TV by taking your MB and phone to a friend's home (or an Apple store) with an

TV and try playing the downloaded files on their

TV. If it works fine on theirs, something in your home is an issue. A great followup test: unhook just your

TV box and take it over to that friend's home. Now try to play the downloaded file from your MB and phone to your

TV (now completely leaning on the friend's network). This eliminates EVERYTHING that can be at fault in your home network setup, testing just the

TV itself to be sure it has no issues.
It's through tests like these that you can narrow in on the problem. Right now, it could be a dozen different things, ranging from any piece of hardware (MB,

TV, router, switch, ethernet cables) to various software issues (different files being fed to different devices, different playback software being used, etc) to user error (are you actually testing the same video head-to-head or different videos?).
Some ideal test videos would be those you know for sure are made for Apple devices- such as movie trailers in iTunes, rather than just any old videos you find out on the web somewhere (which may be mixed in terms of what will play well on Apple hardware). Conceptually, your iPhone is being fed a h.264 MP4 file while your MB might be fed a Flash video version (thus the reason to download a video(s) to sync to the phone so you are testing the exact same video(s) head to head).
I hope this is helpful. This is definitely not a case of phone > computer. The problem you are facing is in the details somewhere. Systematic testing can help you zoom in on the specific thing(s) at fault.