How to distinguish your brand from competing brands if those have a similar selling proposal?

under the given condition it is very important to understand point of parity and point of difference according to your brand.
Point of difference means attributes or benefits consumers strongly associate with a single brand, points where you are claiming superiority or exclusiveness over other products in the category.
Point of parity means associations or attributes that are not necessarily unique to the brand but may be shared by other brands i.e.
where you can at least match the competitors claimed benefits.
While POPs may usually not be the reason to choose a brand, their absence can certainly be a reason to drop a brand.
The main things here is that how marvelously you manage it when it come to placement of the brand in the mind of customer.
Mention some attributes those are common in your brand and competitor’s brand (POPs) then height light some attributes those are exclusive in your brand (PODs)

A well defined Brand Key is generally the distinguishing factor between yourself, and similar brands.
It not only helps define a target market, but assists in focusing our energy into effective product planning, apt management of resources, and strategic marketing to capture only those customers who we know are/will be/will want to be associated to our brand.

In my perspective you have two options

1. To compete with other brand , but first you have to know

every single detail about thier product as if it is your own.

Then try different approach emphasizing their product weakness points, your product strength points, and the most important thing turning your product features into benefits (link it with every day life)

2. I prefer this one, Is to rise above the competition. doing what everyone else does is comfortable and safe, but doing something different it takes courage.

Focus on one aspect of your product and make it the best in your space.

Try different markets like tenders or bids.Think vertically not horizontally (remember the%-% rule that you can get% of your target from% of your customers base).

it is really a good question,I suggest that you focus on your competitive advantage and build a strategy on4Ps that always conveys your superiority for example,in price :give a price that is under the average but push customer to buy more,reduction for4 pieces together,for the product:chose a packaging that show the message that you want to give to the customer (green for bio),contrary to competitor products promote your product in a different way so it will be first in mind ,finaly your product must be always available to take advantage of the shortness of any competitor product

A brand is not based on a USP. 

it should be based on your vision, mission and values. 

You usually use USPs for specific campaigns for specific products. 

Apart from a well devised Brand Management Strategy, a communication strategy is another must.
This will give you a clear picture of who your target market is, how they behave, where they are, and how to engage them.
The communication strategy will then help you decide the best way to get your message across.
After all Advertising is not simply selling--it's getting the consumer to buy from you.

If  your offering is similar to competitor's your brand will bring the additional features that makes the difference from customer's prospective

- identify customers' concerns & criteria

- analyse competitors' brand positioning from customer's prospective

    * identify competitors strong & week points

    * identify your strong and weak points compared to competitors

    * turn your weakness into strengths (an advantage hides an inconvenient and vice versa)

- in front of your customer, position yourself emphasizing all your strengths with several examples to illustrate each of your strengths 

on ajoutant plus  des proposition de vente 

If you are in a market where competition is rude competitors proposing same equipements levels try to work on your sales team motivate them more than your competitors and they will do it for you, besides help them with a good communication plan, this in operational on strategic try to work on your price there are some cents that can make a difference...
may be in logistics costs or in financial cost or somewhere in your production/importation product pre-life.