Not to be nit-picky or anything, but your "question" is not actually phrased as a question. What kind of information are you specifically looking for? For example, are you looking for comparisons only--as in how they are similar, or are you also looking for contrast--as in how they differ from one another? Are you only looking for thematic points--such as they are both Psalms of praise (as opposed to lamentations), or are you interested in comparing the structure of the Psalms themselves--things like length?
Without such information I can't guarantee that you will be satisfied with my answer, but I'll make an attempt.
Both Psalms are praise Psalms which extol various qualities of God. Psalm 103 lists itself as a Psalm of David. The authorship of Psalm 99 is not given. While both list qualities of God, they focus on different ones.
Psalm 99 is the last of the so-called "royal" Psalms in that it not only directly addresses God's kingship, it highlights it and calls on His worshipers to tremble before Him (v. 1). It draws attention to the vast division between man and God. (vs. 1-2) It also focuses on His holiness; the Psalm points this characteristic out no less than three separate times.
Psalm 103 on the other hand, focuses more on God's merciful nature. While it too mentions the fact that God has a throne and a kingdom (v. 19); it spends much more time comparing him to a father and highlighting his mercy (vs. 13-17), while both draw attention to the fact that God is above us and should be feared (99:1 - 103:17), Psalm 103 identifies Him as a father figure (v. 13). Psalm 99 shows that He is separate from humanity while Psalm 103 shows that He is intimately involved with us.
While both Psalms contain similar wording about God's mercy and/or forgiving nature (compare Psalm 99:4 and Psalm 103:6; Psalm 103:7 and Psalm 99:6), and how He has come to the aid of the prophets of old, Psalm 99 is quite a bit more focused on His holy judgement and Psalm 103 on His tender and merciful nature.
1 Bless the LORD, O my soul: and all that is within me, bless his holy name.
2 Bless the LORD, O my soul, and forget not all his benefits:
3 Who forgiveth all thine iniquities; who healeth all thy diseases;
4 Who redeemeth thy life from destruction; who crowneth thee with lovingkindness and tender mercies;
5 Who satisfieth thy mouth with good things; so that thy youth is renewed like the eagle's.
6 The LORD executeth righteousness and judgment for all that are oppressed.
7 He made known his ways unto Moses, his acts unto the children of Israel.
8 The LORD is merciful and gracious, slow to anger, and plenteous in mercy.
9 He will not always chide: neither will he keep his anger for ever.
10 He hath not dealt with us after our sins; nor rewarded us according to our iniquities.
11 For as the heaven is high above the earth, so great is his mercy toward them that fear him.
12 As far as the east is from the west, so far hath he removed our transgressions from us.
13 Like as a father pitieth his children, so the LORD pitieth them that fear him.
14 For he knoweth our frame; he remembereth that we are dust.
15 As for man, his days are as grass: as a flower of the field, so he flourisheth.
16 For the wind passeth over it, and it is gone; and the place thereof shall know it no more.
17 But the mercy of the LORD is from everlasting to everlasting upon them that fear him, and his righteousness unto children's children;
18 To such as keep his covenant, and to those that remember his commandments to do them.
19 The LORD hath prepared his throne in the heavens; and his kingdom ruleth over all.
20 Bless the LORD, ye his angels, that excel in strength, that do his commandments, hearkening unto the voice of his word.
21 Bless ye the LORD, all ye his hosts; ye ministers of his, that do his pleasure.
22 Bless the LORD, all his works in all places of his dominion: bless the LORD, O my soul.1
in psalm 99 it is a psalm of david