I am inclined to understand that the current wisdom is that there's a certain period right after exercise where protein consumption is most beneficial. At work, which is where I generally get my exercise right after my workday, I have a bag of milled flax seed that I use as a snack during the day. I know that not all proteins are equal, and that vegetable proteins tend to have fewer of the amino acids one needs. I do normally consume the usual amount of meat for someone in the United States (that is to say, too much), and flax seed seems to be well thought-of in terms of being a protein source, but I'm curious as to whether it's beneficial for this particular purpose.
You are ok with the flax seed, as it is a complete protein. It's not as high a source of protein as beef, as it comes in at 19 grams protein per 100 grams (Beef is 26, chicken is 30).
The common wisdom is that protein is protein as far as the body is concerned, and to a large extent that is true. A plant protein produces many (but not all) of the same effects in the body as a meat protein, with many of the same outcomes (calcium leeching from bones, etc).
However, what does have to be taken into consideration is what happens in the body with what gets bundled with the protein, such as fiber, healthy/unhealthy fat, salt, and newer items such as heterocyclic amines (HCA) and polycyclic aromatic hydrocarbons (PAH), which the US based National Institute of Health have now put on their list of items "reasonable expected to be a human carcinogen". (Fact sheet on grilled meats)
This study short reaches the same conclusion, in that the protein reacts in the same way in the body regardless of source, but that what comes along with it causes different body responses.
This study short performed two different trials on plasma cholesterol in women when substituting soy protein, and in both cases, plasma cholesterol was lower on the more plant based diet, suggesting that the fats that come along with meat proteins have a detrimental effect on the body.
The Harvard School of Public Health has a pretty good writeup on protein as well.
To summarize, if you eat the flax seed, you may not get as much protein as you would from a meat source, but it may have other benefits that the meat wouldn't, especially if you already do consume animal proteins at other time. I wasn't able to find a study that compared body response to protein source post workout specifically.