You provided a lot of information . . . most of it (with all due respect) meaningless. And you left out the one critical detail.
Asking price of $153,9000: Irrelevant. (The house might be worth more or less than that.)
Two other offers: Irrelevant. (You don't know the interests or motivations of the other bidders.)
Cash offers from investors: Irrelevant. (Now there's a bit of information. But the investors' motivations likely are far different than yours. Also, they're looking at the numbers differently. Even if the house were worth $153,900, it might not make economic sense for an investor to pay that.)
Your financial details: Irrelevant. (OK. YOU have been told that you'll likely qualify for the loan. But the bank will be weighing two cash offers against one with financing.)
Look: The only relevant piece of data is what the house is worth. You pay no more than that. Depending on your strategy, you might offer that amount or you might offer less.
Does a cash offer always come in lower than the asking price? Absolutely not. Suppose a property is worth $170,000. It's priced at $153,900. Someone paying cash might well offer something above $153,900. In fact, sometimes foreclosures are intentially listed low in order to generate buying frenzy.
Should you have gone higher? Depends on what the house is worth and, secondarily, how much you and your wife wanted the house. Suppose it's worth $170,000. If you and your wife loved the house (and were prequalified or preapproved for a higher amount), maybe you could have offered $160,000 or $165,000. On the other hand, suppose it's only worth $140,000. In that case, your maximum bid should have been $140,000 or less.
What would be the typical cash offer on a house with an asking price of $153,900? Depends. If it's worth $153,900, the investor will then look at his/her exit strategy. Rehab and resell? Rent out for cash flow? With rehab and resell, many investors would offer less. Renting out for cash flow, it all depends on what that property would bring in as a rental.
As you can see, the real question is: What is the house worth? And what it's worth to you as a "retail buyer" may be quite different from what it's worth to an investor.
All you can do is approach it as a retail buyer.
You're second-guessing yourself. But if you want to explore the issue further, take a look at what your Realtor said the house was worth.
Hope that helps.