The great difference between the two poems lies in the way the poet perceives himself on coming to God. Taylor sees himself as wretched and weak; Tennyson, while giving some acknowledgement of sinfulness, comes as a “saint”.

Psalm 6 is also a poem of coming to God, which begins:

Psalm 6:1–3 (AV)

¹ O LORD, rebuke me not in thine anger, neither chasten me in thy hot displeasure. ² Have mercy upon me, O LORD; for I am weak: O LORD, heal me; for my bones are vexed. ³ My soul is also sore vexed: but thou, O LORD, how long?

Charles Spurgeon, in The Treasury of David, writes:

“Have mercy upon me, O Lord; for I am weak.” Though I deserve destruction, yet let thy mercy pity my frailty. This is the right way to plead with God if we would prevail. Urge not your goodness or your greatness, but plead your sin and your littleness. Cry, “I am weak,” therefore O Lord, give me strength and crush me not. Send not forth the fury of thy tempest against so weak a vessel. Temper the wind to the shorn lamb. Be tender and pitiful to a poor withering flower, and break it not from, its stem. Surely this is the plea that a sick man would urge to move the pity of his fellow if he were striving with him, “Deal gently with me, ‘for I am weak.’ ” A sense of sin had so spoiled the Psalmist’s pride, so taken away his vaunted strength, that he found himself weak to obey the law, weak through the sorrow that was in him, too weak, perhaps, to lay hold on the promise. “I am weak.” The original may be read, “I am one who droops,” or withered like a blighted plant. Ah! beloved, we know what this means, for we, too, have seen our glory stained, and our beauty like a faded flower.

And so, while not the only thing to say on the topic, Edward Taylor has come in the vein of the one who was weak.