”トムはもう食べてしまっている。”
Tom has already eaten.

As compared to:
トム は もう 食べてしまった 。
Tom has already eaten.

”トムはもう食べてしまっている。” has a stronger emphasis on the completion of having eaten. To me, Tom does not seem to just have eaten but has eaten some time ago.

e.g.
1)トムは空腹だ。　しかし、昼食にと持ってきたものをトムはもう食べてしまっている。
Tom is feeling hungry. But, he have eaten what he had brought with him for lunch. (He ate it some time ago.)

2)トムはお腹が空いた。しかし、昼食にと持ってきたものをトムはもう食べてしまった。
Tom is feeling hungry. But he have just finished what he has brought for lunch already. (He has just finished.)

"トム は もう 食べ た 。"
Simply states that Tom either has eaten or ate.
e.g
1)person A:皆さんもうお昼は食べましたか？　Person B:トムはもう食べた。メアリーはまだ。
Person A: Has everyone had lunch already? Person B: Tom already has. Mary has not yet.

2)トムはもう食べた。メアリーはどうしようか悩んでいる。ビリーは絶対嫌だと拒絶して怒っている。私のペットの死体を料理して食べることで供養するというアイディアはどうも万人受けしないようだ。どうしよう?

Tom has already eaten. Mary is wondering what she should do. Billy has rejected with absolute certainty and angry. It appears my idea: "Cocking and eating our pet who has just left us for the consolation of her soul" is not for everyone. Oh boy, what am I to do?

As the sentence has a simple aspect, it conveys a quick crisp and vivid imagery but is not very informative, no clue given as to what is to come next and the time line of events etc, and depends on the context to provide for those missing pieces.
　

”トムは食べてしまった。”
Describes that the action has either just has completed or has completed sometime ago but its consequences lasting up to the present. Also, ending "しまった" can be used to convey a feeling of regret: "しまっている" does not have a sense like this.

1)トムは食べてしまった。腐った納豆を！！　トムのお腹に明日はあるのか？
Tom has eaten. What he ate: A rotten Natto!! Oh, shall Tom's belly see the light of the day again?

2)トムは食べてしまった。人魚の肉を。アレから十年、トム老いを知らない。　
Tom has eaten the fresh of a mermaid. Ten years since then, age has not touched Tom.

3)トムは昼食を食べてしまった。すると途端にやることが無くなる。無人島は本当に退屈なところである。
Tom has finished his lunch. Then, all of a sudden he's got nothing to do. Really and truelove, an uninhabited island is a boring place.

Note: if the introduction of the subject was delayed, it might be a sign that the object is something the author would like to present as significant.
So, it is relatively usual to write or say:
"トムは食べてしまった。夕食を。"
It's comical, or tragic if Tom has not eaten dinner so long and eating it means so much for him now.