it's who gives the gift that's important

 V'anisa v'amarta....  

The Tiferes Shlomo writes derech remez that a person has to be an ani b'daas and approach Hashem with humility.  This is the essence of what bringing bikurim is all about -- recognizing that if it wasn't for chasdei Hashem, none of the crops would be there.

(As a general rule, it's probably a good idea to have a little "v'anisa" of humilty before opening your mouth "v'amarta" to voice your opinion.)

The Mishna tells us that the rich would bring bikurim in expensive gold and silver baskets which the kohanim would return, while the poor would bring bikurim in simple baskets which the kohanim would then keep.  There is a similar account brought by the gemara (M"K 27a) with respect to food brought to a mourner's house: the rich would bring the food on gold and silver trays, the poor would bring simple platters. There the gemara says that the Chachamim made a takanah that everyone should bring the same simple platters so as to not embarrass the poor.  Why was there such a takanah made with respect to the beis ha'avel but not with respect to bikurim?

R' Mordechai Eliyahu answers based on the Sefer haChinuch that the whole essence of the mitzvah of bikurim is to recognize that everything -- whether you have a lot of money or a little money -- is yad Hashem.  If you have that perspective, then you can't feel bad about being poor and you can't let being rich go to your head.  Had Chazal made a takanah to level the playing field of gifts, they would be undermining the whole essence of what the mitzvah is all about (he gives other answers in his sefer as well).

"V'samachta b'kol ha'tuv asher nasan lecha Hashem Elokecha..."  The secret to happiness is recognizing the "...asher nasan lecha Hashem Elokecha" in everything.  It's not what you have which is important -- it's who is giving it to you.

The Midrash Tanchuma writes that Moshe saw that there would be a churban ha'bayis and there would be no more bikurim so he made a takana to daven three times a day.  (See Rambam hil tefilah 1:5 who says davening 3x a day was a takanah of Ezra's beis din; see R' Nisim Gaon in Shabbos 30a who does not list tefilah as one of the takanos of Moshe.)  Like bikurim, tefilah is all about the recognition of Hashem as the source of everything we have.

(I think you also see from this Chazal that tefilah is not about asking for things, but rather it's about giving.  When you bring bikurim you have to bring something to the mikdash, not ask for something to take home with you.  Similarly, tefilah is a replacement for korbanos.  A korban is something you bring, not something you ask for or get.  What do we bring when we offer a tefilah?  Foremost, we bring ourselves and our committment.)