No studies show conclusive evidence that testosterone makes one more aggressive or competitive (and, as far as I know, researchers haven't even attempted to connect androgens to competitiveness; women are often very competative, too, just often in different ways and about different things.) Some FTMs report increased aggression, but many do not; it's possible that they only feel more comfortable expressing aggression because it is expected or because they simply feel more comfortable with themselves, thus not too shy to be aggressive/assertive. It seems reliable that estrogen causes what might be described as being "emotional" (since when are "masculine emotions" not emotions?) but that is generally believed to be due to the cyclic nature of female hormone production, which may not apply to MTFs, depending on their regimen. Increases in sensitivity may be due to the psychological factors mentioned above.
Transsexual hormone therapy is also known as Hormone Reassignment Therapy (with the sometimes confusingly identical acronym as for Hormone Replacement Therapy for menopausal women).
Other physical changes that often occur with HRT for female-to-male transsexuals (I'll be onesided since this is my area of knowledge) include...
- Changes in smell in sweat, urine and sexual fluids (many report more of a musky scent)
- Roughening of the skin (complimentarily to what Saige mentions above, softening of skin in MTFs)
- Increased body hair as well as facial hair
- Creation of a more masculine hairline, possible thinning of hair or balding (though usually not until after several years)
- Cessation of menses
- Thinning of vaginal wall/lessening of vaginal lubrication
- Clitoral growth
- Increased sex drive
- Increased risk of heart disease (only to the "male level", as males are considered to have a higher risk of heart disease)
- Decreased risk of osteoporosis
- Softening of breast tissue (some also report a slight decrease in breast size, though I have never heard of it being enough to actually make a difference with regard to hiding or removing them)
- Increased risk of reproductive organ cancer (uterine and ovarian) if they are not removed. This increased risk is caused by the organs lying dormant for a long period of time and is similar to the way that post-menopausal women have an increased risk for this very reason.
The most common "full dose" of testosterone for FTMs is 200mg every two weeks (or the equivalent... some do 100mg every week to provide hormonal consistency) if one is using injections. Almost no FTMs take their hormones orally as it's quite hard on the liver; the most common method is injections, and secondary options include gel (applied to the skin) or a patch (much like a nicotine patch), though the alternatives to injection are considerably more expensive and some people find they irritate the skin.